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给定有限输入x和期望输出d,存在唯一的m+1长的最小平方滤波因子h~(m)=(h_0~(m),h_1~(m),…,h_m~(m)),为简单起见,记上式为q_m~2。一般q_m~2不趋于0(m→∞),只有当x为最小延迟时才有q_m~2→0(m→∞)。这样就限制了最小平方滤波的作用。但在地震数据处理中,有时允许期望输出d延迟其一定出现位置,即以x和为输入和期望输出,当最小平方滤波因子长度为m+1时,对应的误差记为q_m~2(S)。本文的结论有q_(2m)~2(m)→0,(m→∞)。更进一步有其中k>1的任何实数,[km]为km的整数部分。
Given a finite input x and a desired output d, there is a unique m + 1 long minimum square filter factor h ~ (m) = (h_0 ~ (m), h_1 ~ (m), ..., h_m ~ (m) For simplicity, remember that the formula is q_m ~ 2. Generally, q_m ~ 2 does not tend to 0 (m → ∞), q_m ~ 2 → 0 (m → ∞) only when x is the minimum delay. This limits the effect of least squares filtering. However, in the seismic data processing, it is sometimes allowed to delay the expected output d from its certain position, that is, input and output as x and the corresponding error is denoted as q_m ~ 2 (S ). The conclusions of this paper are q_ (2m) ~ 2 (m) → 0, (m → ∞). Further, there is any real number where k> 1, where [km] is the integer part of km.